R Notebook

Call Libraries

library(tidyverse)
library(car)
library(moments)
library(glmnet)

Calling the Transformed Datasets

income_cleaned = read_csv('Shiny_app/data/income_cleaned.csv')

Rows: 1921 Columns: 5── Column specification ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (2): Name, Group
dbl (3): Year, Num, Avg
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

industry_cleaned = read_csv('Shiny_app/data/industry_cleaned.csv')

Rows: 2476 Columns: 5── Column specification ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (2): Name, Group
dbl (3): Year, Num, Avg
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

Creating the Models

sat.model.summary <- function (df, field, sat.formula){
    
    #Shapiro-Wilks test to evaluate normality
    print(shapiro.test(df[[field]]))
    
    #Kurtosis evaluation (normal distribution has a value close to 3)
    print('kurtosis')
    print(kurtosis(df[[field]]))
    linear.model.cleaned = lm(sat.formula, data = df)
    print(summary(linear.model.cleaned))
    plot(linear.model.cleaned)
    
    #histograms of response variable to check distribution
    print(df %>% 
      ggplot(aes_string(field)) + 
      geom_histogram() + 
      labs(title = 'Average Credit Amount Distribution') + 
      theme(plot.title = element_text(hjust = 0.5)))
    
    #Checking multicollinearity using VIF measurement
    print(vif(linear.model.cleaned))
    influencePlot(linear.model.cleaned)
    #avPlots(linear.model.cleaned)
}


sat.formula <- Avg ~ .
sat.field <- 'Avg'

sat.model.summary(income_cleaned, sat.field, sat.formula)

    Shapiro-Wilk normality test

data:  df[[field]]
W = 0.17297, p-value < 2.2e-16

[1] "kurtosis"
[1] 169.7518

Call:
lm(formula = sat.formula, data = df)

Residuals:
      Min        1Q    Median        3Q       Max 
-11338570   -547702     94139    421302  87181761 

Coefficients:
                                                                                                Estimate Std. Error t value Pr(>|t|)    
(Intercept)                                                                                   -1.157e+08  5.512e+07  -2.100  0.03590 *  
Year                                                                                           5.721e+04  2.731e+04   2.095  0.03634 *  
NameAlternative Fuels and Electric Vehicle Recharging Property Credit                         -3.287e+05  1.242e+06  -0.265  0.79140    
NameAlternative Minimum Tax Credit                                                             6.538e+05  9.757e+05   0.670  0.50286    
NameBeer Production Credit                                                                     3.316e+05  1.290e+06   0.257  0.79715    
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 6/23/08 but before 7/1/15  1.429e+06  9.960e+05   1.434  0.15162    
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 7/1/15                     4.098e+06  1.421e+06   2.883  0.00398 ** 
NameBrownfield Tax Credits - Redevelopment Tax Credit - Prior to 6/23/08                       1.182e+06  9.927e+05   1.191  0.23386    
NameBrownfield Tax Credits - Remediation Real Property Tax Credit                             -7.587e+04  9.920e+05  -0.076  0.93904    
NameClean Heating Fuel Credit                                                                  7.148e+04  1.024e+06   0.070  0.94436    
NameConservation Easement Tax Credit                                                           1.143e+05  1.064e+06   0.107  0.91444    
NameCredit for Employment of Persons with Disabilities                                        -9.343e+05  1.119e+06  -0.835  0.40391    
NameCredit for Purchase of an Automated External Defibrillator                                -1.449e+05  9.695e+05  -0.150  0.88117    
NameCredit for Taxicabs & Livery Service Vehicles Accessible to Persons with Disabilities      2.316e+05  1.779e+06   0.130  0.89645    
NameEmpire State Apprentice Tax Credit                                                        -7.983e+05  1.524e+06  -0.524  0.60040    
NameEmpire State Commercial Production Credit                                                  2.183e+05  1.291e+06   0.169  0.86576    
NameEmpire State Film Post Production Credit                                                   2.521e+04  1.049e+06   0.024  0.98082    
NameEmpire State Film Production Credit                                                        1.145e+07  9.967e+05  11.485  < 2e-16 ***
NameEmpire State Musical and Theatrical Production Credit                                     -2.342e+05  1.775e+06  -0.132  0.89507    
NameExcelsior Jobs Program Credit                                                              1.035e+05  9.545e+05   0.108  0.91366    
NameEZ/QEZE Tax Credits - EZ Investment Tax Credit                                             2.752e+06  8.862e+05   3.105  0.00193 ** 
NameEZ/QEZE Tax Credits - EZ Wage Tax Credit                                                   4.845e+05  9.213e+05   0.526  0.59899    
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes                                  1.245e+06  9.239e+05   1.348  0.17785    
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes For Corporate Partners          -1.025e+05  9.549e+05  -0.107  0.91455    
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit                                           -6.145e+04  9.387e+05  -0.065  0.94781    
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit For Corporate Partners                     9.119e+04  1.044e+06   0.087  0.93038    
NameFarm Workforce Retention Credit                                                           -7.802e+03  1.285e+06  -0.006  0.99516    
NameFarmers' School Tax Credit                                                                 1.440e+05  1.021e+06   0.141  0.88786    
NameHire a Veteran Credit                                                                     -1.238e+06  1.782e+06  -0.695  0.48721    
NameHistoric Properties Rehabilitation Credit                                                  1.352e+06  1.055e+06   1.282  0.20015    
NameIndustrial or Manufacturing Business Tax Credit                                            4.997e+05  1.074e+06   0.465  0.64173    
NameInvestment Tax Credit                                                                      4.463e+05  8.895e+05   0.502  0.61588    
NameInvestment Tax Credit for the Financial Services Industry                                  3.976e+05  1.008e+06   0.395  0.69325    
NameLife Sciences Research & Development Tax Credit                                           -8.207e+04  2.099e+06  -0.039  0.96882    
NameLong-Term Care Insurance Credit                                                            1.246e+05  9.808e+05   0.127  0.89892    
NameLow-Income Housing Credit                                                                 -2.764e+04  1.113e+06  -0.025  0.98020    
NameMinimum Wage Reimbursement Credit                                                         -2.931e+05  1.006e+06  -0.291  0.77075    
NameMortgage Servicing Tax Credit                                                             -4.540e+05  1.085e+06  -0.418  0.67565    
NameNew York Youth Jobs Program Tax Credit                                                    -2.587e+05  9.381e+05  -0.276  0.78279    
NameQETC Capital Tax Credit                                                                    2.616e+05  1.386e+06   0.189  0.85032    
NameQETC Employment Credit                                                                     1.335e+05  1.026e+06   0.130  0.89641    
NameQETC Facilities, Operations, and Training Credit                                           5.153e+05  1.918e+06   0.269  0.78820    
NameReal Property Tax Relief Credit for Manufacturing                                         -2.635e+05  9.654e+05  -0.273  0.78490    
NameSpecial Additional Mortgage Recording Tax Credit                                           3.678e+04  9.244e+05   0.040  0.96827    
NameSTART-UP NY Tax Elimination Credit                                                         4.061e+03  1.130e+06   0.004  0.99713    
Group1,000,000 - 24,999,999                                                                    2.170e+05  3.501e+05   0.620  0.53548    
Group100,000 - 499,999                                                                         1.352e+05  3.579e+05   0.378  0.70572    
Group100,000,000 - 499,999,999                                                                 9.644e+05  3.937e+05   2.449  0.01441 *  
Group25,000,000 - 49,999,999                                                                   4.519e+05  4.223e+05   1.070  0.28474    
Group50,000,000 - 99,999,999                                                                   4.021e+05  4.235e+05   0.950  0.34247    
Group500,000 - 999,999                                                                         2.195e+05  3.880e+05   0.566  0.57170    
Group500,000,000 - and over                                                                    3.073e+06  3.846e+05   7.991 2.33e-15 ***
GroupZero or Net Loss                                                                          9.536e+05  3.339e+05   2.856  0.00433 ** 
Num                                                                                           -4.520e+02  8.569e+02  -0.527  0.59791    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3868000 on 1867 degrees of freedom
Multiple R-squared:  0.2361,    Adjusted R-squared:  0.2144 
F-statistic: 10.88 on 53 and 1867 DF,  p-value: < 2.2e-16

          GVIF Df GVIF^(1/(2*Df))
Year  2.125869  1        1.458036
Name  3.521453 43        1.014746
Group 1.510763  8        1.026124
Num   1.645484  1        1.282764

income.model <- lm(sat.formula, data = income_cleaned)

sat.model.summary(industry_cleaned, sat.field, sat.formula)

    Shapiro-Wilk normality test

data:  df[[field]]
W = 0.22287, p-value < 2.2e-16

[1] "kurtosis"
[1] 135.5482

Call:
lm(formula = sat.formula, data = df)

Residuals:
      Min        1Q    Median        3Q       Max 
-11581741   -371031    -23164    154182  28917959 

Coefficients:
                                                                                                Estimate Std. Error t value Pr(>|t|)    
(Intercept)                                                                                   -3.926e+07  2.051e+07  -1.914 0.055677 .  
Year                                                                                           1.936e+04  1.016e+04   1.905 0.056959 .  
NameAlternative Fuels and Electric Vehicle Recharging Property Credit                          5.584e+04  5.062e+05   0.110 0.912180    
NameAlternative Minimum Tax Credit                                                             3.523e+05  4.208e+05   0.837 0.402556    
NameBeer Production Credit                                                                     8.799e+04  6.261e+05   0.141 0.888249    
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 6/23/08 but before 7/1/15  1.919e+06  4.473e+05   4.290 1.86e-05 ***
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 7/1/15                     4.064e+06  7.278e+05   5.584 2.62e-08 ***
NameBrownfield Tax Credits - Redevelopment Tax Credit - Prior to 6/23/08                       1.054e+06  4.779e+05   2.206 0.027462 *  
NameBrownfield Tax Credits - Remediation Real Property Tax Credit                              1.327e+05  4.760e+05   0.279 0.780429    
NameClean Heating Fuel Credit                                                                  2.785e+05  4.595e+05   0.606 0.544549    
NameConservation Easement Tax Credit                                                           2.743e+04  4.700e+05   0.058 0.953457    
NameCredit for Employment of Persons with Disabilities                                         1.574e+05  5.069e+05   0.311 0.756142    
NameCredit for Purchase of an Automated External Defibrillator                                 1.082e+05  4.465e+05   0.242 0.808639    
NameCredit for Taxicabs & Livery Service Vehicles Accessible to Persons with Disabilities      2.090e+05  8.286e+05   0.252 0.800866    
NameEmpire State Apprentice Tax Credit                                                        -3.324e+05  1.012e+06  -0.329 0.742537    
NameEmpire State Commercial Production Credit                                                  3.524e+05  6.172e+05   0.571 0.568123    
NameEmpire State Film Post Production Credit                                                   5.332e+05  5.224e+05   1.021 0.307585    
NameEmpire State Film Production Credit                                                        1.170e+07  4.785e+05  24.458  < 2e-16 ***
NameEmpire State Musical and Theatrical Production Credit                                      7.676e+04  9.010e+05   0.085 0.932112    
NameExcelsior Jobs Program Credit                                                              7.086e+05  4.393e+05   1.613 0.106849    
NameEZ/QEZE Tax Credits - EZ Investment Tax Credit                                             1.381e+06  4.318e+05   3.199 0.001399 ** 
NameEZ/QEZE Tax Credits - EZ Wage Tax Credit                                                   3.715e+05  4.213e+05   0.882 0.377942    
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes                                  1.160e+06  4.192e+05   2.767 0.005700 ** 
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes For Corporate Partners           3.634e+05  4.311e+05   0.843 0.399359    
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit                                            2.567e+05  4.265e+05   0.602 0.547350    
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit For Corporate Partners                     7.379e+04  5.041e+05   0.146 0.883634    
NameFarm Workforce Retention Credit                                                            2.727e+04  5.352e+05   0.051 0.959361    
NameFarmers' School Tax Credit                                                                 1.287e+05  5.133e+05   0.251 0.802102    
NameHire a Veteran Credit                                                                      1.459e+05  8.253e+05   0.177 0.859709    
NameHistoric Properties Rehabilitation Credit                                                  1.875e+06  4.841e+05   3.874 0.000110 ***
NameInvestment Tax Credit                                                                      7.182e+05  4.129e+05   1.739 0.082075 .  
NameInvestment Tax Credit for the Financial Services Industry                                  6.339e+05  5.757e+05   1.101 0.270913    
NameLife Sciences Research & Development Tax Credit                                           -2.243e+03  9.007e+05  -0.002 0.998014    
NameLong-Term Care Insurance Credit                                                            1.385e+05  4.200e+05   0.330 0.741537    
NameLow-Income Housing Credit                                                                  1.642e+06  5.494e+05   2.988 0.002833 ** 
NameMinimum Wage Reimbursement Credit                                                          9.624e+04  4.381e+05   0.220 0.826159    
NameMortgage Servicing Tax Credit                                                              2.077e+05  6.462e+05   0.321 0.747934    
NameNew York Youth Jobs Program Tax Credit                                                     1.953e+05  4.273e+05   0.457 0.647604    
NameQETC Capital Tax Credit                                                                    2.986e+05  5.868e+05   0.509 0.610823    
NameQETC Employment Credit                                                                     8.982e+04  4.465e+05   0.201 0.840607    
NameQETC Facilities, Operations, and Training Credit                                           3.477e+05  6.711e+05   0.518 0.604441    
NameReal Property Tax Relief Credit for Manufacturing                                          1.520e+05  4.423e+05   0.344 0.731171    
NameSpecial Additional Mortgage Recording Tax Credit                                           2.609e+05  4.432e+05   0.589 0.556155    
NameSTART-UP NY Tax Elimination Credit                                                         1.703e+04  4.750e+05   0.036 0.971411    
GroupAdministrative and Support and Waste Management and Remediation Services                 -2.280e+03  2.519e+05  -0.009 0.992777    
GroupAdministrative/Support/Waste Management/Remediation Services                             -3.173e+03  2.798e+05  -0.011 0.990952    
GroupAgriculture, Forestry, Fishing and Hunting                                                7.269e+04  2.330e+05   0.312 0.755097    
GroupArts, Entertainment, and Recreation                                                       5.866e+05  2.317e+05   2.532 0.011408 *  
GroupConstruction                                                                             -1.699e+04  2.171e+05  -0.078 0.937621    
GroupEducational Services                                                                      5.569e+04  2.948e+05   0.189 0.850176    
GroupFinance and Insurance                                                                     2.139e+05  2.034e+05   1.051 0.293237    
GroupHealth Care and Social Assistance                                                         1.300e+04  2.290e+05   0.057 0.954731    
GroupInformation                                                                              -2.433e+05  2.178e+05  -1.117 0.263917    
GroupManagement of Companies and Enterprises                                                   3.355e+05  1.949e+05   1.721 0.085332 .  
GroupManufacturing                                                                             6.786e+05  2.028e+05   3.346 0.000831 ***
GroupMining                                                                                   -1.561e+04  3.593e+05  -0.043 0.965352    
GroupMining, Quarrying, and Oil and Gas Extraction                                             1.084e+05  3.011e+05   0.360 0.718901    
GroupOther Services (except Public Administration)                                            -6.462e+04  2.217e+05  -0.291 0.770697    
GroupProfessional, Scientific, and Technical Services                                          3.736e+05  2.085e+05   1.792 0.073214 .  
GroupReal Estate and Rental and Leasing                                                        9.506e+04  2.044e+05   0.465 0.641882    
GroupRetail Trade                                                                              4.746e+04  2.036e+05   0.233 0.815756    
GroupTransportation and Warehousing                                                           -1.866e+04  2.300e+05  -0.081 0.935321    
GroupUtilities                                                                                 5.308e+05  2.633e+05   2.016 0.043917 *  
GroupWholesale Trade                                                                           6.106e+04  2.081e+05   0.293 0.769261    
Num                                                                                           -9.657e+02  4.272e+02  -2.260 0.023889 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1612000 on 2411 degrees of freedom
Multiple R-squared:  0.4674,    Adjusted R-squared:  0.4533 
F-statistic: 33.06 on 64 and 2411 DF,  p-value: < 2.2e-16

          GVIF Df GVIF^(1/(2*Df))
Year  2.190806  1        1.480137
Name  5.185764 42        1.019787
Group 2.724217 20        1.025371
Num   1.370920  1        1.170863

industry.model <- lm(sat.formula, data = industry_cleaned)

Selecting Specific Diagnostic plots for linear models

plot(income.model, which = 1)

plot(income.model, which = 2)

plot(income.model, which = 3)

plot(income.model, which = 5)

Correcting violation of Normality in previous model with BoxCox transform

bc_func <- function (lm.cleaned, lambda.range){
  bc = boxCox(lm.cleaned, lambda = lambda.range)
  #Extracting the best lambda value.
  return(bc$x[which(bc$y == max(bc$y))])
}

#Income Group Dataset
income.lambda.bc = bc_func(income.model, seq(-0.2, 0.2, 1/10))

income.lambda.bc

[1] -0.01414141

#Industry Group Dataset
industry.lambda.bc = bc_func(industry.model, seq(-0.2, 0.2, 1/10))

industry.lambda.bc

[1] -0.03434343

bc_transform <- function(df, lambda.bc){
  return (df %>% 
            mutate(Avg.bc = (Avg^lambda.bc -1)/lambda.bc) %>% 
            select(-c(Avg))) #took out field Amount
}

#Income Group Dataset
income_cleaned_bc <- bc_transform(income_cleaned, income.lambda.bc)
income.model.bc = lm(Avg.bc ~ ., data = income_cleaned_bc)

#Industry Group Dataset
industry_cleaned_bc <- bc_transform(industry_cleaned, industry.lambda.bc)
industry.model.bc = lm(Avg.bc ~ ., data = industry_cleaned_bc)

Testing out appending a newly created dataframe to a list of dataframes with a Name for Shiny app

# income_cleaned_bc
# all.data <- list('income_cleaned' = income_cleaned, 'industry_cleaned' = industry_cleaned)
# all.data <- append(all.data, list('income_cleaned_bc' = income_cleaned_bc))
# all.data[['income_cleaned_bc']]

Testing out bc_func for migration to Shiny App global.R file

bc_funct <- function (df, lm.cleaned, lambda.range){
  bc = boxCox(lm.cleaned, lambda = lambda.range)
  lambda.bc = bc$x[which(bc$y == max(bc$y))]
  return(df %>% 
            mutate(Avg.bc = (Avg^lambda.bc -1)/lambda.bc) %>% 
            select(-c(Avg)))
}

bc_funct(income_cleaned, income.model, seq(-0.2, 0.2, 1/10))

Checking linear regression assumptions for the transformed data.

sat.formula.bc <- Avg.bc ~ .
sat.field.bc <- 'Avg.bc'

#Income
sat.model.summary(income_cleaned_bc, sat.field.bc, sat.formula.bc)

    Shapiro-Wilk normality test

data:  df[[field]]
W = 0.99696, p-value = 0.000782

[1] "kurtosis"
[1] -0.2553313

Call:
lm(formula = sat.formula, data = df)

Residuals:
    Min      1Q  Median      3Q     Max 
-6.6597 -0.5738 -0.0113  0.5668  4.4826 

Coefficients:
                                                                                                Estimate Std. Error t value Pr(>|t|)    
(Intercept)                                                                                   -3.634e+01  1.456e+01  -2.496 0.012643 *  
Year                                                                                           2.288e-02  7.214e-03   3.171 0.001543 ** 
NameAlternative Fuels and Electric Vehicle Recharging Property Credit                         -8.643e-01  3.281e-01  -2.634 0.008510 ** 
NameAlternative Minimum Tax Credit                                                            -2.052e+00  2.577e-01  -7.962 2.91e-15 ***
NameBeer Production Credit                                                                     5.687e-01  3.407e-01   1.669 0.095234 .  
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 6/23/08 but before 7/1/15  1.715e+00  2.630e-01   6.521 8.99e-11 ***
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 7/1/15                     2.676e+00  3.754e-01   7.130 1.43e-12 ***
NameBrownfield Tax Credits - Redevelopment Tax Credit - Prior to 6/23/08                       1.331e+00  2.622e-01   5.076 4.24e-07 ***
NameBrownfield Tax Credits - Remediation Real Property Tax Credit                              5.458e-02  2.620e-01   0.208 0.834991    
NameClean Heating Fuel Credit                                                                 -3.086e+00  2.705e-01 -11.409  < 2e-16 ***
NameConservation Easement Tax Credit                                                          -2.137e+00  2.810e-01  -7.606 4.45e-14 ***
NameCredit for Employment of Persons with Disabilities                                        -3.118e+00  2.956e-01 -10.547  < 2e-16 ***
NameCredit for Purchase of an Automated External Defibrillator                                -2.938e+00  2.560e-01 -11.473  < 2e-16 ***
NameCredit for Taxicabs & Livery Service Vehicles Accessible to Persons with Disabilities     -5.673e-01  4.698e-01  -1.207 0.227430    
NameEmpire State Apprentice Tax Credit                                                        -2.207e+00  4.024e-01  -5.485 4.71e-08 ***
NameEmpire State Commercial Production Credit                                                  6.075e-02  3.410e-01   0.178 0.858634    
NameEmpire State Film Post Production Credit                                                   1.101e+00  2.769e-01   3.977 7.25e-05 ***
NameEmpire State Film Production Credit                                                        2.853e+00  2.632e-01  10.838  < 2e-16 ***
NameEmpire State Musical and Theatrical Production Credit                                      2.508e-01  4.688e-01   0.535 0.592803    
NameExcelsior Jobs Program Credit                                                              4.651e-01  2.521e-01   1.845 0.065178 .  
NameEZ/QEZE Tax Credits - EZ Investment Tax Credit                                             8.876e-01  2.341e-01   3.792 0.000154 ***
NameEZ/QEZE Tax Credits - EZ Wage Tax Credit                                                   1.775e-01  2.433e-01   0.730 0.465701    
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes                                  1.220e+00  2.440e-01   5.000 6.26e-07 ***
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes For Corporate Partners           1.182e-01  2.522e-01   0.469 0.639260    
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit                                           -8.497e-01  2.479e-01  -3.427 0.000623 ***
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit For Corporate Partners                    -1.358e+00  2.756e-01  -4.928 9.02e-07 ***
NameFarm Workforce Retention Credit                                                           -1.612e+00  3.394e-01  -4.749 2.20e-06 ***
NameFarmers' School Tax Credit                                                                -1.311e+00  2.696e-01  -4.863 1.26e-06 ***
NameHire a Veteran Credit                                                                     -2.915e+00  4.706e-01  -6.195 7.15e-10 ***
NameHistoric Properties Rehabilitation Credit                                                  1.918e+00  2.786e-01   6.886 7.81e-12 ***
NameIndustrial or Manufacturing Business Tax Credit                                           -1.718e+00  2.836e-01  -6.059 1.66e-09 ***
NameInvestment Tax Credit                                                                      7.147e-02  2.349e-01   0.304 0.760985    
NameInvestment Tax Credit for the Financial Services Industry                                  3.176e-01  2.662e-01   1.193 0.232870    
NameLife Sciences Research & Development Tax Credit                                            7.033e-01  5.543e-01   1.269 0.204728    
NameLong-Term Care Insurance Credit                                                           -2.863e+00  2.590e-01 -11.051  < 2e-16 ***
NameLow-Income Housing Credit                                                                 -9.063e-01  2.940e-01  -3.083 0.002080 ** 
NameMinimum Wage Reimbursement Credit                                                         -1.241e+00  2.656e-01  -4.674 3.17e-06 ***
NameMortgage Servicing Tax Credit                                                             -9.378e-01  2.865e-01  -3.273 0.001084 ** 
NameNew York Youth Jobs Program Tax Credit                                                    -1.330e+00  2.478e-01  -5.367 9.01e-08 ***
NameQETC Capital Tax Credit                                                                    4.561e-01  3.661e-01   1.246 0.212956    
NameQETC Employment Credit                                                                    -5.888e-01  2.709e-01  -2.174 0.029855 *  
NameQETC Facilities, Operations, and Training Credit                                           5.799e-01  5.065e-01   1.145 0.252462    
NameReal Property Tax Relief Credit for Manufacturing                                         -1.518e+00  2.550e-01  -5.956 3.09e-09 ***
NameSpecial Additional Mortgage Recording Tax Credit                                          -2.309e-01  2.441e-01  -0.946 0.344374    
NameSTART-UP NY Tax Elimination Credit                                                        -2.193e+00  2.985e-01  -7.345 3.05e-13 ***
Group1,000,000 - 24,999,999                                                                    1.090e+00  9.246e-02  11.785  < 2e-16 ***
Group100,000 - 499,999                                                                         3.590e-01  9.451e-02   3.798 0.000150 ***
Group100,000,000 - 499,999,999                                                                 1.685e+00  1.040e-01  16.202  < 2e-16 ***
Group25,000,000 - 49,999,999                                                                   1.325e+00  1.115e-01  11.883  < 2e-16 ***
Group50,000,000 - 99,999,999                                                                   1.473e+00  1.118e-01  13.172  < 2e-16 ***
Group500,000 - 999,999                                                                         6.032e-01  1.025e-01   5.886 4.67e-09 ***
Group500,000,000 - and over                                                                    2.332e+00  1.016e-01  22.953  < 2e-16 ***
GroupZero or Net Loss                                                                          9.934e-01  8.817e-02  11.267  < 2e-16 ***
Num                                                                                           -1.533e-03  2.263e-04  -6.775 1.66e-11 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.022 on 1867 degrees of freedom
Multiple R-squared:  0.7368,    Adjusted R-squared:  0.7293 
F-statistic: 98.61 on 53 and 1867 DF,  p-value: < 2.2e-16

          GVIF Df GVIF^(1/(2*Df))
Year  2.125869  1        1.458036
Name  3.521453 43        1.014746
Group 1.510763  8        1.026124
Num   1.645484  1        1.282764

#Industry
sat.model.summary(industry_cleaned_bc, sat.field.bc, sat.formula.bc)

    Shapiro-Wilk normality test

data:  df[[field]]
W = 0.9902, p-value = 5.826e-12

[1] "kurtosis"
[1] -0.4869026

Call:
lm(formula = sat.formula, data = df)

Residuals:
    Min      1Q  Median      3Q     Max 
-6.2888 -0.4697  0.0183  0.4928  3.9068 

Coefficients:
                                                                                                Estimate Std. Error t value Pr(>|t|)    
(Intercept)                                                                                   -6.095e+01  1.107e+01  -5.505 4.09e-08 ***
Year                                                                                           3.440e-02  5.488e-03   6.269 4.30e-10 ***
NameAlternative Fuels and Electric Vehicle Recharging Property Credit                          2.665e-01  2.733e-01   0.975 0.329737    
NameAlternative Minimum Tax Credit                                                            -2.463e+00  2.272e-01 -10.839  < 2e-16 ***
NameBeer Production Credit                                                                     6.334e-01  3.381e-01   1.873 0.061126 .  
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 6/23/08 but before 7/1/15  2.198e+00  2.415e-01   9.100  < 2e-16 ***
NameBrownfield Tax Credits - Redevelopment Tax Credit - On or after 7/1/15                     2.727e+00  3.930e-01   6.939 5.06e-12 ***
NameBrownfield Tax Credits - Redevelopment Tax Credit - Prior to 6/23/08                       1.586e+00  2.581e-01   6.148 9.17e-10 ***
NameBrownfield Tax Credits - Remediation Real Property Tax Credit                              9.695e-01  2.570e-01   3.772 0.000166 ***
NameClean Heating Fuel Credit                                                                 -2.544e+00  2.481e-01 -10.252  < 2e-16 ***
NameConservation Easement Tax Credit                                                          -1.123e+00  2.538e-01  -4.423 1.02e-05 ***
NameCredit for Employment of Persons with Disabilities                                        -1.245e+00  2.737e-01  -4.549 5.67e-06 ***
NameCredit for Purchase of an Automated External Defibrillator                                -1.535e+00  2.411e-01  -6.368 2.29e-10 ***
NameCredit for Taxicabs & Livery Service Vehicles Accessible to Persons with Disabilities     -8.171e-02  4.474e-01  -0.183 0.855119    
NameEmpire State Apprentice Tax Credit                                                        -8.683e-01  5.464e-01  -1.589 0.112125    
NameEmpire State Commercial Production Credit                                                  6.235e-01  3.333e-01   1.871 0.061481 .  
NameEmpire State Film Post Production Credit                                                   1.439e+00  2.821e-01   5.100 3.66e-07 ***
NameEmpire State Film Production Credit                                                        3.232e+00  2.584e-01  12.509  < 2e-16 ***
NameEmpire State Musical and Theatrical Production Credit                                      1.012e+00  4.865e-01   2.080 0.037608 *  
NameExcelsior Jobs Program Credit                                                              1.643e+00  2.372e-01   6.929 5.42e-12 ***
NameEZ/QEZE Tax Credits - EZ Investment Tax Credit                                             1.310e+00  2.332e-01   5.617 2.17e-08 ***
NameEZ/QEZE Tax Credits - EZ Wage Tax Credit                                                   7.127e-01  2.275e-01   3.133 0.001750 ** 
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes                                  1.707e+00  2.264e-01   7.540 6.61e-14 ***
NameEZ/QEZE Tax Credits - QEZE Credit for Real Property Taxes For Corporate Partners           9.777e-01  2.328e-01   4.200 2.77e-05 ***
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit                                            1.609e-01  2.303e-01   0.699 0.484921    
NameEZ/QEZE Tax Credits - QEZE Tax Reduction Credit For Corporate Partners                    -5.241e-01  2.722e-01  -1.925 0.054320 .  
NameFarm Workforce Retention Credit                                                           -8.623e-01  2.890e-01  -2.984 0.002876 ** 
NameFarmers' School Tax Credit                                                                -1.158e+00  2.771e-01  -4.179 3.03e-05 ***
NameHire a Veteran Credit                                                                     -1.040e+00  4.456e-01  -2.335 0.019638 *  
NameHistoric Properties Rehabilitation Credit                                                  2.397e+00  2.614e-01   9.172  < 2e-16 ***
NameInvestment Tax Credit                                                                      6.981e-01  2.230e-01   3.131 0.001763 ** 
NameInvestment Tax Credit for the Financial Services Industry                                  1.560e+00  3.108e-01   5.019 5.59e-07 ***
NameLife Sciences Research & Development Tax Credit                                            9.057e-01  4.864e-01   1.862 0.062697 .  
NameLong-Term Care Insurance Credit                                                           -1.867e+00  2.268e-01  -8.231 3.01e-16 ***
NameLow-Income Housing Credit                                                                  1.331e+00  2.967e-01   4.487 7.57e-06 ***
NameMinimum Wage Reimbursement Credit                                                         -9.161e-01  2.366e-01  -3.872 0.000111 ***
NameMortgage Servicing Tax Credit                                                              8.932e-01  3.489e-01   2.560 0.010534 *  
NameNew York Youth Jobs Program Tax Credit                                                     1.263e-01  2.307e-01   0.548 0.584069    
NameQETC Capital Tax Credit                                                                    1.162e+00  3.168e-01   3.667 0.000251 ***
NameQETC Employment Credit                                                                    -3.048e-01  2.411e-01  -1.264 0.206249    
NameQETC Facilities, Operations, and Training Credit                                           1.147e+00  3.624e-01   3.165 0.001571 ** 
NameReal Property Tax Relief Credit for Manufacturing                                         -6.559e-01  2.388e-01  -2.746 0.006077 ** 
NameSpecial Additional Mortgage Recording Tax Credit                                           7.505e-01  2.393e-01   3.136 0.001736 ** 
NameSTART-UP NY Tax Elimination Credit                                                        -1.834e+00  2.565e-01  -7.151 1.14e-12 ***
GroupAdministrative and Support and Waste Management and Remediation Services                  2.878e-01  1.360e-01   2.116 0.034417 *  
GroupAdministrative/Support/Waste Management/Remediation Services                              1.675e-01  1.511e-01   1.109 0.267612    
GroupAgriculture, Forestry, Fishing and Hunting                                               -1.132e-01  1.258e-01  -0.899 0.368486    
GroupArts, Entertainment, and Recreation                                                       5.595e-01  1.251e-01   4.473 8.09e-06 ***
GroupConstruction                                                                             -4.299e-02  1.172e-01  -0.367 0.713860    
GroupEducational Services                                                                      2.253e-01  1.592e-01   1.415 0.157160    
GroupFinance and Insurance                                                                     5.350e-01  1.099e-01   4.870 1.19e-06 ***
GroupHealth Care and Social Assistance                                                        -6.777e-02  1.237e-01  -0.548 0.583720    
GroupInformation                                                                               7.098e-01  1.176e-01   6.037 1.81e-09 ***
GroupManagement of Companies and Enterprises                                                   6.672e-01  1.052e-01   6.340 2.73e-10 ***
GroupManufacturing                                                                             4.608e-01  1.095e-01   4.208 2.67e-05 ***
GroupMining                                                                                    2.515e-01  1.940e-01   1.296 0.194977    
GroupMining, Quarrying, and Oil and Gas Extraction                                             3.869e-01  1.626e-01   2.379 0.017421 *  
GroupOther Services (except Public Administration)                                            -1.550e-01  1.197e-01  -1.295 0.195482    
GroupProfessional, Scientific, and Technical Services                                          4.875e-01  1.126e-01   4.331 1.55e-05 ***
GroupReal Estate and Rental and Leasing                                                        1.461e-01  1.104e-01   1.324 0.185596    
GroupRetail Trade                                                                              3.754e-01  1.100e-01   3.414 0.000650 ***
GroupTransportation and Warehousing                                                            2.125e-01  1.242e-01   1.711 0.087179 .  
GroupUtilities                                                                                 6.972e-01  1.422e-01   4.904 1.00e-06 ***
GroupWholesale Trade                                                                           4.367e-01  1.124e-01   3.886 0.000105 ***
Num                                                                                            4.542e-04  2.307e-04   1.969 0.049082 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.8703 on 2411 degrees of freedom
Multiple R-squared:  0.7631,    Adjusted R-squared:  0.7569 
F-statistic: 121.4 on 64 and 2411 DF,  p-value: < 2.2e-16

          GVIF Df GVIF^(1/(2*Df))
Year  2.190806  1        1.480137
Name  5.185764 42        1.019787
Group 2.724217 20        1.025371
Num   1.370920  1        1.170863

avPlots(income.model.bc)

NA

NA

NA

NA
NA

BIC comparison before and after BoxCox transform

BIC(income.model.bc, income.model)

BIC(industry.model.bc, industry.model)

Stepwise Regression on Income_cat_bc (boxcox transformed dataset)

#creating dummy variable columns for stepwise
dummy_func <- function (df){
  x = model.matrix(Avg.bc ~., df)[, -1]
  dummy_bc = as.data.frame(x) %>% mutate(Avg.bc = df$Avg.bc)
  #colnames(dummy_bc) <- str_replace_all(colnames(dummy_bc), "-|'|/| |,|�|&" , '_')
  colnames(dummy_bc) <- str_replace_all(colnames(dummy_bc), "[-'/ ,�&()`]" , '_')
  return(dummy_bc)
}

Cleaning column names further so stepwise regression doesn’t present any errors

#Income Group Dataset
income.dummy.bc <- dummy_func(income_cleaned_bc)
#colnames(income.dummy.bc)[37] <- 'NameManufactureru0092s_Real_Property_Tax_Credit'
colnames(income.dummy.bc)

#Industry Group Dataset
industry.dummy.bc <- dummy_func(industry_cleaned_bc)
#colnames(industry.dummy.bc)[35] <- 'NameManufactureru0092s_Real_Property_Tax_Credit'
colnames(industry.dummy.bc)

Stepwise regression using BIC as the criteria (k = log(n)).

#Creating Stepwise Models
bcs = list(income = income.dummy.bc, industry = industry.dummy.bc)
model.fulls = list(income = lm(Avg.bc ~ ., data = income.dummy.bc), industry = lm(Avg.bc ~ ., data = industry.dummy.bc)) #All variables
model.emptys = list(income = lm(Avg.bc ~ 1, data = income.dummy.bc), industry = lm(Avg.bc ~ 1, data = industry.dummy.bc)) #intercept only
k = c('income', 'industry')
forwardBIC = list(income = NULL, industry = NULL)
backwardBIC = list(income = NULL, industry = NULL)

for (i in k){
  bc = bcs[[i]]
  scope = list(lower = formula(model.emptys[[i]]), upper = formula(model.fulls[[i]]))
  n_obs = bc %>% count() %>% dplyr::first()
  forwardBIC[[i]] = step(model.emptys[[i]], scope, direction = "forward", k = log(n_obs))
  backwardBIC[[i]] = step(model.fulls[[i]], scope, direction = "backward", k = log(n_obs))
}

Selecting Best Formula per Dataset from Stepwise Regressions

bic_func(forwardBIC[['income']])

[1] "Adjusted R Squared:"

Error in summary(BIC.model) : object 'forwardBIC' not found

Best Model Selection from Stepwise

#The Best Models selected for both income and industry were forwardBIC.

#Income Group Dataset
income.best.formula <- forwardBIC[['income']]$call[[2]]
income.best.formula

#Industry Group Dataset
industry.best.formula <- forwardBIC[['industry']]$call[[2]]
industry.best.formula

Splitting data up into test data and training data (test data is for year 2019, training is the rest)

test_train_split <- function(dummy_bc, best.formula) {
  # data.test <- dummy_bc %>% filter(Year == 2019)
  # data.train <- dummy_bc %>% filter(Year != 2019)
  X <- model.matrix(best.formula, data = dummy_bc)[,-1]
  y <- as.matrix(dummy_bc %>% select(all.vars(best.formula)[1]))
  
  set.seed(0)
  train.i = sample(1:nrow(dummy_bc), 0.8*nrow(dummy_bc), replace = F)
  
  #train
  X.train <- X[train.i,]
  y.train <- y[train.i,]
  
  #test
  X.test <- X[-train.i,]
  y.test <- y[-train.i,]
  
  data.train <- as.data.frame(cbind(y.train, X.train))
  data.test <- as.data.frame(cbind(y.test, X.test))
  colnames(data.train)[1] = all.vars(best.formula)[1]
  colnames(data.test)[1] = all.vars(best.formula)[1]
  
  return (list('X.train' = X.train, 'y.train' = y.train, 'X.test' = X.test, 'y.test' = y.test, 'data.train' = data.train, 'data.test' = data.test))
}

test_train_split_old <- function(dummy_bc, best.formula) {
  # data.test <- dummy_bc %>% filter(Year == 2019)
  # data.train <- dummy_bc %>% filter(Year != 2019)
  set.seed(0)
  train.i = sample(1:nrow(dummy_bc), 0.8*nrow(dummy_bc), replace = F)
  data.train <- dummy_bc %>% slice(train.i)
  data.test <- dummy_bc %>% slice(-train.i)
  
  #train
  #X.train <- as.matrix(data.train %>% select(-Avg.bc))
  X.train <- model.matrix(best.formula, data = data.train)[,-1]
  y.train <- as.matrix(data.train %>% select(all.vars(best.formula)[1]))

  #test
  #X.test <- as.matrix(data.test %>% select(-Avg.bc))
  X.test <- model.matrix(best.formula, data = data.test)[,-1]
  y.test <- as.matrix(data.test %>% select(all.vars(best.formula)[1]))
  
  #return (list('X.train' = X.train, 'y.train' = y.train, 'X.test' = X.test, 'y.test' = y.test, 'data.train' = data.train, 'data.test' = data.test))
}

#Income
income.data.split.sat <- test_train_split(income.dummy.bc, Avg.bc ~ .)
income.data.split <- test_train_split(income.dummy.bc, income.best.formula)

#Industry
industry.data.split.sat <- test_train_split(industry.dummy.bc, Avg.bc ~ .)
industry.data.split <- test_train_split(industry.dummy.bc, industry.best.formula)

test_train_split(income_cleaned, sat.formula)

Lasso regression for comparison to Forward Stepwise

# calc_MSE <- function (model, x.test, y.test){
#   y.predict <- predict(model, newdata = x.test)
#   return(mean((y.predict - y.test)^2))
# }

# xy.splits <- list('income' = income.data.split, 
#                   'industry' = industry.data.split, 
#                   'income.sat' = income.data.split.sat, 
#                   'industry.sat' = industry.data.split.sat)
# 
# lasso.list <- c('income', 'industry', 'income.sat', 'industry.sat')
# baseline.list <- c('income.sat', 'industry.sat', 'income.sat', 'industry.sat')
# ridge.alpha <- 0
# 
# for (a in 1:4){
#   i = lasso.list[a]
#   b = baseline.list[a]
#   X.train <- xy.splits[[i]][['X.train']]
#   y.train <- xy.splits[[i]][['y.train']]
#   X.test <- xy.splits[[i]][['X.test']]
#   y.test <- xy.splits[[i]][['y.test']]
#   X.test.sat <- xy.splits[[b]][['X.test']]
#   y.test.sat <- xy.splits[[b]][['y.test']]
#   data.train <- xy.splits[[i]][['data.train']]
#   data.test <- xy.splits[[i]][['data.test']]
#   
#   #create lambda grid
#   lambda.grid = 10^seq(2, -5, length = 100)
#   
#   #create lasso models with lambda.grid
#   lasso.models = glmnet(X.train, y.train, alpha = ridge.alpha, lambda = lambda.grid)
#   
#   #visualize coefficient shrinkage
#   plot(lasso.models, xvar = "lambda", label = TRUE, main = paste("Lasso Regression:", i))
#   
#   #Cross Validation to find best lambda
#   set.seed(0)
#   cv.lasso.models <- cv.glmnet(X.train, y.train, alpha = ridge.alpha, lambda = lambda.grid, nfolds = 10)
#   
#   #visualize cross validation for lambda that minimizes the mean squared error.
#   plot(cv.lasso.models, main = paste("Lasso Regression:", i))
#   
#   #Checking the best lambda
#   log(cv.lasso.models$lambda.min)
#   best.lambda <- cv.lasso.models$lambda.min
#   print(paste(i, ' best.lambda:', best.lambda))
#   # best lambda with all the variables was found to be 0.0006892612
#   # best lambda with only the bwdBIC coefficients included was found to be 0.0003053856
#   
#   #looking at the lasso coefficients for the best.lambda
#   best.lambda.coeff <- predict(lasso.models, s = best.lambda, type = "coefficients")
#   print('Number of Coefficients:')
#   print(dim(best.lambda.coeff)[1])
#   
#   #fitting a model with the best lambda found to be 0.000689 and using it to make predictions for the testing data.
#   lasso.best.lambda.train.pred <- predict(lasso.models, s = best.lambda, newx = X.test)
#   lasso.best.lambda.train.pred
#   
#   #checking MSE
#   MSE.lasso <- mean((lasso.best.lambda.train.pred - y.test)^2)
#   sat.model.bc <- lm(Avg.bc ~., data = data.train)
#   
#   
#   temp.df <- as.data.frame(X.test.sat) #temp fix
#   colnames(temp.df) <- str_replace_all(colnames(temp.df), "[`]", '')
#   
#   y.predict <- predict(sat.model.bc, newdata = temp.df)
#   MSE.sat <- mean((y.predict - y.test.sat)^2)
#   
#   print(paste(i, ' Lasso MSE: ', MSE.lasso, ' ', b, ' Saturated MSE: ', MSE.sat))
# 
#   metrics <- eval_results(y.test, lasso.best.lambda.train.pred, data.test)
#   print(metrics)
#   print('********************************')
# }

Function to show metrics (R^2 and MSE) for Regularization (Ridge/Lasso)

regularization_func <- function (data, alpha, name){
  X.train <- data[['X.train']]
  y.train <- data[['y.train']]
  X.test <- data [['X.test']]
  y.test <- data[['y.test']]
  data.test <- data[['data.test']]
  # print(colnames(X.train))
  # print(colnames(X.test))
  # print(setdiff(colnames(X.train), colnames(X.test)))
  
  #create lambda grid
  lambda.grid = 10^seq(10, -10, length = 100)
  
  #create lasso models with lambda.grid
  lasso.models = glmnet(X.train, y.train, alpha = alpha, lambda = lambda.grid)
  
  #visualize coefficient shrinkage
  # plot(lasso.models, xvar = "lambda", label = TRUE, main = paste("Lasso Regression:", i))
  
  #Cross Validation to find best lambda
  set.seed(0)
  cv.lasso.models <- cv.glmnet(X.train, y.train, alpha = alpha, lambda = lambda.grid, nfolds = 10)
  
  #visualize cross validation for lambda that minimizes the mean squared error.
  plot(cv.lasso.models, main = paste("Alpha:", alpha, "Regression:", name))
  
  #Checking the best lambda
  # log(cv.lasso.models$lambda.min)
  # best.lambda <- cv.lasso.models$lambda.min
  # print(paste(i, ' best.lambda:', best.lambda))
  # best lambda with all the variables was found to be 0.0006892612
  # best lambda with only the bwdBIC coefficients included was found to be 0.0003053856
  
  #looking at the lasso coefficients for the best.lambda
  # best.lambda.coeff <- predict(lasso.models, s = cv.lasso.models$lambda.min, type = "coefficients")
  # print('Number of Coefficients:')
  # print(dim(best.lambda.coeff)[1])
  
  #fitting a model with the best lambda found to be 0.000689 and using it to make predictions for the testing data.
  lasso.best.lambda.train.pred <- predict(lasso.models, s = cv.lasso.models$lambda.min, newx = X.test)
  lasso.best.lambda.train.pred
  
  #checking MSE
  MSE.lasso <- mean((lasso.best.lambda.train.pred - y.test)^2)
  print(paste('Dimensions of the Alpha:', alpha, ' Regression Coefficients for:', name))
  print(dim(coef(lasso.models))[1])
  p = dim(coef(lasso.models))[1]
  return(eval_results(y.test, lasso.best.lambda.train.pred, data.test, p)['Rsquare'])
}
regularization_func(all.splits[['income_cleaned']], 0, 'income_cleaned')

Warning: collapsing to unique 'x' valuesWarning: collapsing to unique 'x' valuesWarning: collapsing to unique 'x' valuesWarning: collapsing to unique 'x' valuesWarning: collapsing to unique 'x' valuesWarning: collapsing to unique 'x' valuesWarning: collapsing to unique 'x' valuesWarning: collapsing to unique 'x' valuesWarning: collapsing to unique 'x' valuesWarning: collapsing to unique 'x' values

[1] "Dimensions of the Alpha: 0  Regression Coefficients for: income_cleaned"
[1] 54
    Rsquare 
-0.01019062 

regularization_func(all.splits[['income_cleaned_bc']], 0, 'income_cleaned_bc')

Warning: collapsing to unique 'x' valuesWarning: collapsing to unique 'x' valuesWarning: collapsing to unique 'x' valuesWarning: collapsing to unique 'x' valuesWarning: collapsing to unique 'x' valuesWarning: collapsing to unique 'x' valuesWarning: collapsing to unique 'x' valuesWarning: collapsing to unique 'x' valuesWarning: collapsing to unique 'x' valuesWarning: collapsing to unique 'x' values

[1] "Dimensions of the Alpha: 0  Regression Coefficients for: income_cleaned_bc"
[1] 54
  Rsquare 
0.6750177 

regularization_func(all.splits[['income.data.split.sat']], 0, 'income.data.split.sat')

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[1] "Dimensions of the Alpha: 0  Regression Coefficients for: income.data.split.sat"
[1] 54
  Rsquare 
0.6750177 

#all.dfs <- list(income_cleaned, income_cleaned_bc, income.dummy.bc)

formulas <- list(income_cleaned = sat.formula, 
                 income_cleaned_bc = sat.formula.bc, 
                 income.data.split.sat = sat.formula.bc, 
                 income.data.split.best = income.best.formula,
                 industry_cleaned = sat.formula, 
                 industry_cleaned_bc = sat.formula.bc, 
                 industry.data.split.sat = sat.formula.bc, 
                 industry.data.split.best = industry.best.formula)

all.splits <- list(
  'income_cleaned' = test_train_split(income_cleaned, formulas[['income_cleaned']]),
  'income_cleaned_bc' = test_train_split(income_cleaned_bc, formulas[['income_cleaned_bc']]),
  'income.data.split.sat' = test_train_split(income.dummy.bc, formulas[['income.data.split.sat']]),
  'income.data.split.best' = test_train_split(income.dummy.bc, formulas[['income.data.split.best']]),
  'industry_cleaned' = test_train_split(industry_cleaned, formulas[['industry_cleaned']]),
  'industry_cleaned_bc' = test_train_split(industry_cleaned_bc, formulas[['industry_cleaned_bc']]),
  'industry.data.split.sat' = test_train_split(industry.dummy.bc, formulas[['industry.data.split.sat']]),
  'industry.data.split.best' = test_train_split(industry.dummy.bc, formulas[['industry.data.split.best']])
)

#For loops initialization
no.reg.r2 <- c() 
lasso.reg.r2 <- c()
ridge.reg.r2 <- c()


for (i in names(all.splits)) {
  #no regularization
  m = lm(formulas[[i]], all.splits[[i]][['data.train']])
  #no.reg.r2 <- c(no.reg.r2, summary(m)$adj.r.squared)
  y.predict = predict(m, newdata = as.data.frame(all.splits[[i]][['X.test']]))
  adj.R2 <- eval_results(all.splits[[i]][['y.test']], y.predict, all.splits[[i]][['data.test']], length(coef(m)))['Rsquare']
  no.reg.r2 <- c(no.reg.r2, adj.R2)
  
  #lasso regularization
  lasso.reg.r2 <- c(lasso.reg.r2, regularization_func(all.splits[[i]], 1, i))
  
  #ridge regularization
  ridge.reg.r2 <- c(ridge.reg.r2, regularization_func(all.splits[[i]], 0, i))
}

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[1] "Dimensions of the Alpha: 1  Regression Coefficients for: income_cleaned"
[1] 54

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[1] "Dimensions of the Alpha: 0  Regression Coefficients for: income_cleaned"
[1] 54

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[1] "Dimensions of the Alpha: 1  Regression Coefficients for: income_cleaned_bc"
[1] 54

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[1] "Dimensions of the Alpha: 0  Regression Coefficients for: income_cleaned_bc"
[1] 54

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[1] "Dimensions of the Alpha: 1  Regression Coefficients for: income.data.split.sat"
[1] 54

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[1] "Dimensions of the Alpha: 0  Regression Coefficients for: income.data.split.sat"
[1] 54

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[1] "Dimensions of the Alpha: 1  Regression Coefficients for: income.data.split.best"
[1] 41

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[1] "Dimensions of the Alpha: 0  Regression Coefficients for: income.data.split.best"
[1] 41

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[1] "Dimensions of the Alpha: 1  Regression Coefficients for: industry_cleaned"
[1] 65

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[1] "Dimensions of the Alpha: 0  Regression Coefficients for: industry_cleaned"
[1] 65

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[1] "Dimensions of the Alpha: 1  Regression Coefficients for: industry_cleaned_bc"
[1] 65

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[1] "Dimensions of the Alpha: 0  Regression Coefficients for: industry_cleaned_bc"
[1] 65

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[1] "Dimensions of the Alpha: 1  Regression Coefficients for: industry.data.split.sat"
[1] 65

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[1] "Dimensions of the Alpha: 0  Regression Coefficients for: industry.data.split.sat"
[1] 65

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[1] "Dimensions of the Alpha: 1  Regression Coefficients for: industry.data.split.best"
[1] 42

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[1] "Dimensions of the Alpha: 0  Regression Coefficients for: industry.data.split.best"
[1] 42

df.rsquare <- as.data.frame(cbind('noReg' = no.reg.r2, 'lassoReg' = lasso.reg.r2, 'ridgeReg' = ridge.reg.r2))
rownames(df.rsquare) = names(all.splits)
df.rsquare

# sat.model.bc <- lm(Avg.bc ~., data = xy.splits.sat[['industry']][['data.train']])
# 
# temp.df <- as.data.frame(xy.splits.sat[['industry']][['X.test']])
# 
# colnames(temp.df)[57]
# 
# colnames(temp.df) <- str_replace_all(colnames(temp.df), "[`]", '')
# colnames(temp.df)
# 
# y.predict <- predict(sat.model.bc, newdata = temp.df)
# MSE.sat <- mean((y.predict - xy.splits.sat[['industry']][['y.test']])^2)
# 
# print(paste(i, ' Lasso MSE: ', MSE.lasso, ' Saturated MSE: ', MSE.sat))
# 
# summary(sat.model.bc)$coefficients
# as.data.frame(xy.splits.sat[['industry']][['X.test']]) %>% select(starts_with('`GroupOth'))

# Calculate R squared from true values and predictions
eval_results <- function(true, predicted, df, p) {
  n = nrow(df)
  adj.RSS <- sum((predicted - true)^2)/(n-p-1)
  adj.TSS <- sum((true - mean(true))^2)/(n-1)
  adj.R_square <- 1 - adj.RSS / adj.TSS
  #RMSE = sqrt(RSS/n)
  
  return(c(Rsquare = adj.R_square))
}

#formula for adjusted R^2 found in following link.
#https://www.graphpad.com/guides/prism/latest/curve-fitting/reg_adjusted-r-squared.htm

Additional Calculations

as.data.frame(lasso.best.lambda.train.pred) %>% mutate(Avg_in_dollars = (lasso.best.lambda.train.pred*lambda.bc+1)^(1/lambda.bc))

income.sat.data.split <- test_train_split(income.dummy.bc, Avg.bc ~ .)
income.sat.data.split[['X.train']]

sat.model.bc <- lm(Avg.bc ~., data = as.data.frame(cbind(income.sat.data.split[['X.train']], income.sat.data.split[['y.train']])))
summary(sat.model.bc)

calc_MSE(sat.model.bc, as.data.frame(income.sat.data.split[['X.test']]), income.sat.data.split[['y.test']])


sat.y.predict <- predict(sat.model.bc, newdata = as.data.frame(income.sat.data.split[['X.test']]))
mean((sat.y.predict - income.sat.data.split[['y.test']])^2)